@article{ASNSP_1997_4_24_3_571_0, author = {Bruna, Joaquim and Ortega-Cerd\`a, Joaquim}, title = {On $L^p$-solutions of the {Laplace} equation and zeros of holomorphic functions}, journal = {Annali della Scuola Normale Superiore di Pisa - Classe di Scienze}, pages = {571--591}, publisher = {Scuola normale superiore}, volume = {Ser. 4, 24}, number = {3}, year = {1997}, zbl = {0893.31003}, mrnumber = {1612330}, language = {en}, url = {http://www.numdam.org/item/ASNSP_1997_4_24_3_571_0/} }
TY - JOUR AU - Bruna, Joaquim AU - Ortega-Cerdà, Joaquim TI - On $L^p$-solutions of the Laplace equation and zeros of holomorphic functions JO - Annali della Scuola Normale Superiore di Pisa - Classe di Scienze PY - 1997 DA - 1997/// SP - 571 EP - 591 VL - Ser. 4, 24 IS - 3 PB - Scuola normale superiore UR - http://www.numdam.org/item/ASNSP_1997_4_24_3_571_0/ UR - https://zbmath.org/?q=an%3A0893.31003 UR - https://www.ams.org/mathscinet-getitem?mr=1612330 LA - en ID - ASNSP_1997_4_24_3_571_0 ER -
Bruna, Joaquim; Ortega-Cerdà, Joaquim. On $L^p$-solutions of the Laplace equation and zeros of holomorphic functions. Annali della Scuola Normale Superiore di Pisa - Classe di Scienze, Série 4, Tome 24 (1997) no. 3, pp. 571-591. http://www.numdam.org/item/ASNSP_1997_4_24_3_571_0/
[And] Solution formulas for the ∂ ∂-equation and weighted Nevanlinna classes in the polydisc, Bull. Soc. Math. France 109 (1985), 135-154. | Zbl 0598.32007
,[Bel1] Zeros of AP functions and related classes of analytic functions, Israel J. Math. 22 (1975) 68-80. | MR 385103 | Zbl 0322.30028
,[Bel2] Factorization for non-Nevanlinna classes of analytic functions, Israel J. Math. 27 (1977), 320-330. | MR 442234 | Zbl 0361.30012
,[Bel1] A duality theorem for harmonic functions, Michigan Math. J. 29 (1982), 123-128. | MR 646379 | Zbl 0482.31004
,[Ber] Carleson type inequalities, Lecture Notes in Math. 1277, Springer-Verlag, pp. 42-55.
, ∂b and[BH] Zero sets and random zero sets in certain function spaces, J. Analyse Math. 64 (1994), 203-217. | MR 1303512 | Zbl 0819.30003
- ,[Bom] A Blaschke-type product and random zero sets for Bergman spaces, Ark. Mat. 30 (1992), 45-60. | MR 1171094 | Zbl 0764.30029
,[CMS] Some new function spaces and their application to harmonic analysis, J. Funct. Anal. 62 (1985), 304-335. | MR 791851 | Zbl 0569.42016
- - ,[Coc] Random Blaschke products, Trans. Amer. Math. Soc. 322 (1990), 731-755. | MR 1022163 | Zbl 0709.30031
,[DH] Zeros of holomorphic functions of finite order and weighted estimates for solutions of ∂ -problem, Math. Sbornik 107 (1978), 163-174. | Zbl 0392.32001
- ,[Fed] Geometric measure theory, Springer-Verlag, New York, N.Y., 1969. | MR 257325 | Zbl 0176.00801
,[Gar] Bounded analytic functions, Academic Press, New York, N.Y, 1981. | MR 628971 | Zbl 0469.30024
,[Gara] Partial differential equations, second edition, Chelsea Publishing Company, New York, N.Y., 1986. | MR 943117
,[Hei] The zeros offunctions in Nevanlinna's area class, Israel J. Math. 34 (1979), 1-11. | MR 571391 | Zbl 0498.30040
,[HK] Subharmonic functions, Academic Press, London, 1976. | Zbl 0419.31001
- ,[Hor] Some conditions on Bergman spaces zero sets, J. Analyse Math. 62 (1994), 323-348. | MR 1269212 | Zbl 0795.30006
,[Leb] A probabilistic zero condition for the Bergman space, Michigan Math. J. 37 (1990), 427-436. | MR 1077326 | Zbl 0717.30008
,[Lig] On the reproducing kernel for harmonic functions and the space of Bloch harmonic functions on the unit ball of Rn, Studia Math. 87 (1987), 23-32. | MR 924758 | Zbl 0658.31006
,[Lue1] Multipliers of Bergman spaces into Lebesgue spaces, Proc. Edinburgh Math. Soc. (2) 29 (1986), 125-131. | MR 829188 | Zbl 0587.30048
,[Lue2] Trace ideal criteria for Toeplitz operators, J. Funct. Anal. 73 (1987), 345-368. | MR 899655 | Zbl 0618.47018
,[Lue3] Zero sequences for Bergman spaces, to appear in Complex Variables. | MR 1413164 | Zbl 0871.30004
,[Mas] Random sequences with prescribed radii in the unit ball, Complex Variables 31 (1996), 193-211. | MR 1423251 | Zbl 0865.41007
,[MW] Weighted norm inequalities for fractional integrals, Trans. Amer. Math. Soc. 192 (1974), 261-274. | MR 340523 | Zbl 0289.26010
- ,[Ort] Zero sets of holomorphic functions in the bidisc, to appear in Ark. Mat. | MR 1611181 | Zbl 0911.32003
,[Pas] Zeros i interpolació en espais de funcions holomorfes del disc unitat, PhD. Thesis, Universitat Autònoma de Barcelona (March, 1988).
,[Rudin] Function theory in the unit ball of Cn, Springer-Verlag, New York, 1980. | MR 601594 | Zbl 0495.32001
,[Rud] Random interpolating sequences with probability one, Bull. London Math. Soc. 26 (1994), 160-164. | MR 1272302 | Zbl 0831.30020
,[Sha] Quasi-balayage and apriori inequalities, in preparation.
,[Ste] Singular integrals and differentiability properties of functions, Princeton University Press, Princeton, New Jersey, 1970. | MR 290095 | Zbl 0207.13501
,[Swe] Positivity for a strongly coupled elliptic system, J. Geom. Anal. 4 (1994), 121-142. | MR 1274141 | Zbl 0792.35048
,[Zhu] Operator theory in the function spaces, Marcel-Dekker, New York, 1990. | MR 1074007 | Zbl 0706.47019
,